Basically, the more depleted and the healthier the depleted battery, the more amperage it can suck from your alternator.
BUT, the voltage, which is electrical pressure, well the voltage regulator, which controls alternator output, needs to be seeking high pressure/ voltage to feed a depleted battery quickly.
The gauge of wire is important, as the more amps that are flowing, the more resistance to flow there is, and the result is less voltage reaching the battery terminals.
Combine too much circuit resistance, with a voltage reguulator seeking only 13.8v, and very few amps will flow into distant depleted batteries.
So a thicker copper circuit is beneficial, but especially so when the voltage regulator is commanding a system voltage f 14.5 volts.
basically 3 times as many amps will flow into a depleted battery that gets 14.7v at its battery terminals, compared to 13.6.
or a batter way to look at at it is a depleted battery might only need 17 amps to be held at 13.7v, , but it will require 55 amps to be brought to 14.7v.
So thicker cable allows less voltage drop, and more juice to flow into a battery, but the voltage that the voltage regulator is seeking plays a HUGE part in just how much charging of a depleted battery will occur while driving.
an Adjustable voltage regulator is key, for fast effective battery charging, but now always easy to implement, depending on vehicle.
One other ting to keep in mind, is that a well depleted healthy battery, can be fed high amperages and reach 80% charged in an hour or less, but getting from 80% to 100% charged CANNOT be accomplished in less than 3.5 hours, and tha tpresumes the battery being held in the mid 14's, which is extremely unlikely, and lesser voltages will double triple and quadruple that 3.5 hours.
Lead acid batteries Need to regularly be returned to full charge, to live a half way respectale lifespan and be reliable for that lifespan. Relying on the alternator to do this, achieve a regular full charge, is Unwise in the extreme.
Have a way to hook up your house battery to a grid powered charger after any significant depletion and you will get much much more life from your battery.
You can get away with 8awg wire, but the thicker the copper, basically the better the charging will be, but the single biggest factor in alternator charging is dependent on the voltage the vehicles voltage regulator is seeking and holding.
They were never intended to quickly recharge depleted batteries, they were intended to keep a nearly fully charged battery, charged enough to start the vehicle and more importantly, NOT overcharge the battery.
Many vehicles will delcare 13.6v to be fine and dandy, where the distant depleted battery is craving the higher amperage that will flow if 14.7v were reaching the battery terminals.
I have an 89 dodge, whose VR is inside the engine computer.
I have tricked it and run an adjustable voltage regulator with a remote dial on my dashboard, and can choose any damn voltage I want, and my alternator has been witness delivering 112 amps into a well depleted northstar AGM battery, at 2200 rpm.
AGM batteries like Lifeline, Odyssey, and Northstar can accept HUGE charging amperages and actually perform better when these rather extreme currents are available to recharge them when they are discharged to the 50% range or lower. Most other AGMS will recommend no more than 30 amps per 100Ah of battery capacity, and if one gets one of these AGM batteries that list a 30% max charge rate, then one can deliberately choose thinner wire, and this will effectively limit the carging rate should te voltage regulator be seeking 14.7v.
ALL vehicles voltage will vary wildly. What you read after engine stating will not be what you measure after an hour drive. Many vehicles the hotter the alternator gets, the internal voltage regulator asks for lesser voltage reducing the workload on alternator, preventing it from cooking itself, but this reduced voltage is hell on depleted batteries.
Anyway this is a huge topic with many ifs ands or butts.
The wire terminations/ ring terminals are incredibly important for a good low resistance circuit, and for safety.
Beware of copper clad aluminum wiring. it needs to be 30 to 40% thicker than all copper wire to have the same current carrying capability.